Hi and welcome to Android Forums.
Go to your phone settings and find your battery indicator in there. open that up and it should give you a list of running programs and the battery usage for each of them. That may tell you which apps are draining your battery severely.
Did you buy the phone new? If so, have you installed any apps that might be keeping the phone awake? If you did buy the phone new, try a factory reset to see if that helps. Check to make sure the battery is a genuine Samsung battery as on my S3, the after-market battery I bought drained far far quicker than the one that came with the phone.
I sold my S3 some time ago and the battery was one of the reasons it went. Since then I have learned that there are a number of contributing factors that can cause battery drain.
Having GPS and location services on can cause battery drain. So can having the screen at 100% brightness or downloading apps that stop the phone from sleeping (
Wakelock Detector is a great app to check if you have any rogue apps.
GSAM Battery Monitor is a really well respected gauge of battery life too and has the ability to see what apps are causing the most battery drain. Might be worth a check.
You could try a different battery and see if you experience the same drain. If all else fails, take it back to the store from which you bought it and explain your issue to them and see what they say.
It's worth noting that we have a forum dedicated to the S3 here on the forums and you can get expert help on here from the many users of your device. The link to register is in my signature below.
I hope you get it sorted.
